71084 · 5387704 - 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

Description:71084 · 5387704 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p280 : Vogel, Srsieve, SierpinskiRiesel, OpenPFGW
Decimal Digits:270999   (log10 is 270998.31833295)
Rank (*):23320 (digit rank is 1)
Entrance Rank (*):572
Currently on list? (*):no
Submitted:7/4/2010 21:44:36 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):1/20/2013 09:09:52 UTC
Database id:93437
Status Flags:none
Score (*):42.6227 (normalized score 0.1123)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 71084 5 387704 -1 2>&1 [Elapsed time: 9.650 seconds]
modified2020-07-07 22:30:34
created2010-07-04 21:48:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tp -q"71084*5^387704-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 71084*5^387704-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 5+sqrt(3) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(114688,20) to FFT(114688,19) Reduced from FFT(114688,19) to FFT(114688,18) Reduced from FFT(114688,18) to FFT(114688,17) Reduced from FFT(114688,17) to FFT(114688,16) 1800490 bit request FFT size=(114688,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 71084*5^387704-1 is prime! (49436.4021s+0.0716s) [Elapsed time: 13.73 hours]
modified2020-07-07 22:30:34
created2010-07-04 21:53:01

Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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